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Question: a person lent a certain sum of money at 4 % per annum at simple interest and in 8 years the interest amounted to rs . 272 less than the sum lent . what was the sum lent ?
A.400.
B.278.
C.289.
D.500.
e ) 821A.
"p - 272 = ( p * 4 * 8 ) / 100 p = 400 answer : a" | null |
Question: a marketing firm determined that , of 200 households surveyed , 80 used neither brand r nor brand b soap , 60 used only brand r soap , and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 households surveyed used both brands of soap ?
A.15.
B.20.
C.30.
D.40.
e ) 45D.
solution for soap r and soap b ( d ) 40 | null |
Question: the length of the bridge , which a train 150 meters long and travelling at 45 km / hr can cross in 30 seconds , is ?
A.388.
B.267.
C.225.
D.288.
e ) 261C.
"speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 150 + x ) / 30 = 25 / 2 = = > 2 ( 150 + x ) = 750 = = > x = 225 m . answer : c" | null |
Question: if x and y are numbers such that ( x + 4 ) ( y - 4 ) = 0 , what is the smallest possible value of x ^ 2 + y ^ 2
A.0.
B.9.
C.12.
D.16.
e ) 18D.
"from ( x + 4 ) ( y - 4 ) = 0 it follows that either x = - 4 or y = 4 . thus either x ^ 2 = 16 or y ^ 2 = 16 . now , if x ^ 2 = 16 , then the least value of y ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 16 + 0 = 16 . similarly if y ^ 2 = 16 , then the least value of x ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 0 + 16 = 16 . answer : d ." | null |
Question: in the set of positive integers from 1 to 90 , what is the sum of all the odd multiples of 5 ?
A.180.
B.245.
C.320.
D.405.
e ) 450D.
"reduce 1 - 90 5 - 15 - 25 - 35 - 45 - - 55 - - 65 - - 75 - - 85 are valid multiples . add them - - > 405 d" | null |
Question: 1000 men have provisions for 18 days . if 400 more men join them , for how many days will the provisions last now ?
A.12.9.
B.12.8.
C.12.6.
D.12.2.
e ) 12.1B.
1000 * 18 = 1400 * x x = 12.8 answer : b | null |
Question: if f ( f ( n ) ) + f ( n ) = 2 n + 3 , f ( 0 ) = 1 then f ( 2014 ) = ?
A.2015.
B.2088.
C.270.
D.1881.
e ) 1781A.
"f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 β β f ( 1 ) = 3 - 1 = 2 , f ( 1 ) = 2 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 β β f ( 2 ) = 5 - 2 = 3 , f ( 2 ) = 3 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 β β f ( 3 ) = 7 - 3 = 4 , f ( 3 ) = 4 . . . . . . . . . . . . . . f ( 2014 ) = 2015 ans : a" | null |
Question: a , b and c can do a piece of work in 30 days , 30 days and 40 days respectively . they began the work together but c left 4 days before the completion of the work . in how many days was the work completed ?
A.12 days.
B.16 days.
C.18 days.
D.11 days.
e ) 38 daysA.
"one day work of a , b and c = 1 / 30 + 1 / 30 + 1 / 40 = 1 / 11 work done by a and b together in the last 4 days = 4 * ( 1 / 30 + 1 / 30 ) = 4 / 15 remaining work = 11 / 15 the number of days required for this initial work = 8 days . the total number of days required = 4 + 8 = 12 days . answer : a" | null |
Question: a man buys an article for $ 100 . and sells it for $ 110 . find the gain percent ?
A.10 %.
B.15 %.
C.25 %.
D.20 %.
e ) 30 %A.
"c . p . = $ 100 s . p . = $ 110 gain = $ 10 gain % = 10 / 100 * 100 = 10 % answer is a" | null |
Question: a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 854 in 4 years . the sum is :
A.rs . 650.
B.rs . 690.
C.rs . 698.
D.rs . 700.
e ) rs . 740C.
"s . i . for 1 year = rs . ( 854 - 815 ) = rs . 39 . s . i . for 3 years = rs . ( 39 x 3 ) = rs . 117 . principal = rs . ( 815 - 117 ) = rs . 698 . answer : option c" | null |
Question: if the average ( arithmetic mean ) of x + 1 , x + 5 , and x + 9 is 0 , then x =
A.β 5.
B.β 4.
C.β 2.
D.β 1.
e ) 0A.
"( x + 1 + x + 5 + x + 9 ) / 3 = 0 = > 3 x + 15 = 0 = > x = - 5 answer a" | null |
Question: country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 14 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 8 % . if ron imported a $ 14,000 imported car and ended up paying $ 1440 in taxes , what is the first tier ' s price level ?
A.$ 1600.
B.$ 5333.
C.$ 6050.
D.$ 7050.
e ) $ 8000B.
"let t be the tier price , p be total price = 14000 per the given conditions : 0.14 t + 0.08 ( p - t ) = 1440 - - - - > t = 5333 . b is the correct answer ." | null |
Question: what should be added to 4750 so that it may become a perfect square ?
A.11.
B.15.
C.16.
D.17.
e ) 18A.
"69 x 69 = 4761 4761 - 4750 = 11 if added to 11 get perfect square answer = a" | null |
Question: john makes $ 60 a week from his job . he earns a raise andnow makes $ 72 a week . what is the % increase ?
A.20 %.
B.16.66 %.
C.16.56 %.
D.17.66 %.
e ) 18.1 %A.
"increase = ( 12 / 60 ) * 100 = ( 1 / 5 ) * 100 = 20 % . a" | null |
Question: 50 + 5 * 12 / ( 180 / 3 ) = ?
A.23.
B.78.
C.27.
D.51.
e ) 81D.
"explanation : 50 + 5 * 12 / ( 180 / 3 ) = 50 + 5 * 12 / ( 60 ) = 50 + ( 5 * 12 ) / 60 = 50 + 1 = 51 . answer : d" | null |
Question: find number which is 50 % less than 60 .
A.18.
B.30.
C.32.
D.26.
e ) 98B.
explanation : 50 % less is 50 % of the given number therefore , 50 % of 60 is 30 . answer : b | null |
Question: mark bought a set of 6 flower pots of different sizes at a total cost of $ 7.80 . each pot cost 0.25 more than the next one below it in size . what was the cost , in dollars , of the largest pot ?
A.$ 1.75.
B.$ 1.93.
C.$ 2.00.
D.$ 2.15.
e ) $ 2.30B.
this question can be solved with a handful of different algebra approaches ( as has been shown in the various posts ) . since the question asks for the price of the largest pot , and the answers are prices , we can test the answers . we ' re told that there are 6 pots and that each pot costs 25 cents more than the next . the total price of the pots is $ 8.25 . we ' re asked for the price of the largest ( most expensive ) pot . since the total price is $ 7.80 ( a 25 - cent increment ) and the the difference in sequential prices of the pots is 25 cents , the largest pot probably has a price that is a 25 - cent increment . from the answer choices , i would then test answer c first ( since answers b and d are not in 25 - cent increments ) . if . . . . the largest pot = $ 1.75 the other 5 pots are . . . . 1.75 1.50 1.25 1.00 0.75 total = $ 7.80 so this must be the answer . b | null |
Question: a certain basketball team that has played 2 / 3 of its games has a record of 18 wins and 2 losses . what is the greatest number of the remaining games that the team can lose and still win at least 3 / 4 of all of its games ?
A.7.
B.6.
C.5.
D.4.
e ) 3C.
"18 wins , 2 losses - total 20 games played . the team has played 2 / 3 rd of all games so total number of games = 30 3 / 4 th of 30 is 22.5 so the team must win 23 games and can afford to lose at most 7 total games . it has already lost 2 games so it can lose another 5 at most . answer ( c )" | null |
Question: a circular well with a diameter of 2 metres , is dug to a depth of 10 metres . what is the volume of the earth dug out ?
A.32 m 3.
B.31.4 m 3.
C.40 m 3.
D.44 m 3.
e ) noneB.
"solution volume = Ο r 2 h βΉ = βΊ ( 22 / 7 Γ 1 Γ 1 Γ 10 ) m 3 βΉ = βΊ 31.4 m 3 . answer b" | null |
Question: a sum fetched a total simple interest of $ 4241.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ?
A.$ 8829.
B.$ 2840.
C.$ 6578.
D.$ 7782.
e ) $ 8930E.
"e 8930 principal = $ 100 x 4241.25 / 9 x 5 = $ 424125 / 45 = $ 8930 ." | null |
Question: the unit digit in the product ( 635 * 767 * 984 * 489 ) is :
A.0.
B.8.
C.3.
D.2.
e ) 1A.
"explanation : unit digit in the given product = unit digit in ( 5 * 7 * 4 * 9 ) = 0 answer : a" | null |
Question: in a survey of political preferences , 78 % of those asked were in favour of at least one of the proposals : i , ii and iii . 50 % of those asked favoured proposal i , 30 % favoured proposal ii , and 20 % favoured proposal iii . if 5 % of those asked favoured all 3 of the proposals , what x percentage of those asked favoured more than one of the 3 proposals .
A.10.
B.12.
C.17.
D.22.
e ) 30C.
bunuel , my answer for exactly 2 people was 17 and this was my approach : 100 % = ( a + b + c ) - ( anb + anc + bnc ) - 5 % + 22 % which leads me to x = 100 % = ( 50 + 30 + 20 ) - ( at least 2 people ) - 5 % + 22 % . c | null |
Question: a certain bag contains 60 balls β 22 white , 18 green , 2 yellow , 15 red , and 3 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?
A.0.7.
B.0.15.
C.0.54.
D.0.85.
e ) 0.91A.
"according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 22 + 18 + 2 ) / 60 = 42 / 60 = 0.7 . answer : a ." | null |
Question: if the personal income tax rate is lowered from 38 % to 30 % , what is the differential savings for a tax payer having an annual income before tax to the tune of $ 36500 ?
A.$ 1825.
B.$ 5000.
C.$ 3150.
D.$ 7000.
e ) $ 10000A.
"saving = ( 38 - 33 ) % of 36500 = 1825 . answer : a" | null |
Question: elvin ' s monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for internet service . elvin ' s total telephone bill for january was $ 48 and elvin ' s total telephone bill for february was 90 $ . if elvin ' s charge for the calls he made in february was twice the charge for the calls he made in january , what is elvin ' s fixed monthly charge for internet service ?
A.$ 5.
B.$ 10.
C.$ 14.
D.$ 6.
e ) $ 28D.
"bill = fixed charge + charge of calls made in jan , bill = fixed charge ( let , y ) + charge of calls made in jan ( let , x ) = $ 48 in feb , bill = fixed charge ( let , y ) + charge of calls made in feb ( then , 2 x ) = $ 90 i . e . x + y = 48 and 2 x + y = 90 take the difference if two equations i . e . ( 2 x + y ) - ( x + y ) = 90 - 48 i . e . x = 42 i . e . fixed monthly charge , y = 6 answer : option d" | null |
Question: in the recent , climate conference in new york , out of 500 men , 300 women , 500 children present inside the building premises , 10 % of the men , 60 % of the women and 70 % of the children were indians . find the percentage of people who were not indian ?
A.59.54 %.
B.66.25 %.
C.55.39 %.
D.63.21 %.
e ) 64.22 %C.
"solution : number of indians men present there = 500 * 10 / 100 = 50 indian women = 300 * 60 / 100 = 180 indian children = 500 * 70 / 100 = 350 . total member present in climate conference = 500 + 300 + 500 = 1300 total indian = 50 + 180 + 350 = 580 hence , % of indian present there = 580 * 100 / 1300 = 44.61 % % of people who were not indian = 100 - 44.61 = 55.39 % . answer c" | null |
Question: two numbers are in the ratio of 5 : 8 . if 30 be subtracted from each , they are in the ratio of 5 : 9 . find the numbers ?
A.122,195.
B.121,199.
C.120,192.
D.102,192.
e ) 126,109C.
"( 5 x - 30 ) : ( 8 x - 30 ) = 5 : 9 x = 24 = > 120,192 answer : c" | null |
Question: find k if 56 / k = 4 .
A.16.
B.17.
C.18.
D.14.
e ) 13D.
"since 56 / k = 4 and 56 / 14 = 4 , then k = 14 correct answer d" | null |
Question: a car traveled from san diego to san francisco at an average speed of 45 miles per hour . if the journey back took twice as long , what was the average speed of the trip ?
A.30 ..
B.32 ..
C.36 ..
D.42 ..
e ) 44 .A.
"let the time taken be = x one way distance = 45 x total distance traveled = 2 * 45 x = 90 x total time taken = x + 2 x = 3 x average speed = 90 x / 3 x = 30 answer : a" | null |
Question: a 400 meter long train crosses a man standing on the platform in 10 sec . what is the speed of the train ?
A.144.
B.108.
C.278.
D.126.
e ) 112A.
"s = 400 / 10 * 18 / 5 = 144 kmph answer : a" | null |
Question: a man took a loan from a bank at the rate of 9 % p . a . simple interest . after 3 years he had to pay rs . 5400 interest only for the period . the principal amount borrowed by him was :
A.rs . 2000.
B.rs . 10,000.
C.rs . 15,000.
D.rs . 20,000.
e ) noneD.
"solution principal = rs . ( 100 x 5400 / 9 x 3 ) = rs . 20000 . answer d" | null |
Question: what is the value of ( 44444445 * 88888885 * 44444442 + 44444438 / 44444444 ^ 2 )
A.88888883.
B.88888884.
C.88888885.
D.88888886.
e ) 88888873A.
"let x = 44444444 , then 44444445 = x + 1 88888885 = 2 x - 3 44444442 = x - 2 44444438 = x - 6 44444444 ^ 2 = x ^ 2 then substitute it in equation ( x + 1 ) ( 2 x - 3 ) ( x - 2 ) + ( x - 6 ) / x ^ 2 ans is 2 x - 5 i . e 88888883 answer : a" | null |
Question: jack spent 1 / 6 of his lifetime in adolescence . his facial hair started growing after 1 / 12 more of his life . he successfully married his girlfriend diana after 1 / 7 more of his life . their son was born after 5 years from then . the son lived just 1 / 2 of what jack lived . jack dies 4 years after his son died . how long did jack live ?
A.75.
B.90.
C.45.
D.80.
e ) 84E.
e 84 explanation : let us assume that jack lived for p years . p / 6 + p / 12 + p / 7 + 5 + p / 2 + 4 = x = > p = 84 . therefore , jack lived for 84 years . | null |
Question: if 7 a - 3 b = 10 b + 40 = - 12 b - 2 a , what is the value of 9 a + 9 b ?
A.- 5.
B.- 3.
C.0.
D.3.
e ) 5C.
( i ) 7 a - 13 b = 40 ( ii ) 2 a + 22 b = - 40 adding ( i ) and ( ii ) : 9 a + 9 b = 0 the answer is c . | null |
Question: the price of a book is increased from $ 300 to $ 420 . what is the % of increase in its price ?
A.10 %.
B.20 %.
C.40 %.
D.50 %.
e ) 60 %C.
"explanation : change in the price = rs 420 Γ’ β¬ β rs 300 = rs 120 percentage of increase = change in the price initial price * 100 . percentage increase in price = ( 120 300 ) * 100 = 40 % c" | null |
Question: a train 210 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 140 m long ?
A.40 sec.
B.50 sec.
C.44 sec.
D.49 sec.
e ) 28 secE.
"speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 210 + 140 = 350 m required time = 350 * 2 / 25 = 28 sec answer : e" | null |
Question: the total price of a basic computer and printer are $ 2,500 . if the same printer had been purchased with an enhanced computer whose price was $ 500 more than the price of the basic computer , then the price of the printer would have been 1 / 8 of that total . what was the price of the basic computer ?
A.1500.
B.1600.
C.1750.
D.1900.
e ) 2125E.
"let the price of basic computer be c and the price of the printer be p : c + p = $ 2,500 . the price of the enhanced computer will be c + 500 and total price for that computer and the printer will be 2,500 + 500 = $ 3,000 . now , we are told that the price of the printer is 1 / 8 of that new total price : p = 1 / 8 * $ 3,000 = $ 375 . plug this value in the first equation : c + 375 = $ 2,500 - - > c = $ 2,125 . answer : e ." | null |
Question: 39 ! is divided by 41 then what is the remainder ?
A.1.
B.2.
C.4.
D.6.
e ) 7A.
"substituting p = 41 in the wilson ' s theorem , we get 40 ! + 141 = 0 40 Γ 39 ! + 141 = 0 β 1 Γ 39 ! 41 = β 1 cancelling - 1 on both sides , 39 ! 41 = 1 a" | null |
Question: if x is equal to the sum of the integers from 10 to 30 , inclusive , and y is the number of even integers from 10 to 30 , inclusive , what is the value of x + y ?
A.401.
B.411.
C.421.
D.431.
e ) 441D.
"x = 10 + 11 + . . . + 30 = 21 ( 20 ) = 420 y = 11 x + y = 431 the answer is d ." | null |
Question: the product of two numbers is 4107 . if the h . c . f . of these numbers is 37 , then the greater number is : explanation :
A.101.
B.107.
C.111.
D.117.
e ) 121C.
let the numbers be 37 a and 37 b . then , 37 a x 37 b = 4107 ab = 3 . now , co - primes with product 3 are ( 1 , 3 ) . so , the required numbers are ( 37 x 1 , 37 x 3 ) i . e . , ( 37 , 111 ) . greater number = 111 . answer : option c | null |
Question: if 42.36 = k ( 14 + m / 50 ) , where k and m are positive integers and m < 50 , then what is the value of k + m ?
A.6.
B.7.
C.8.
D.9.
e ) 10D.
"42.36 = 14 k + km / 50 . . . we can rewrite the number as follows : 42 + 0.36 = 14 k + km / 50 . . . . . . . . since k is integer , then 42 = 14 k . . . . . . . . . . k = 3 0.36 = km / 50 . . . . . . 36 / 100 = 3 m / 50 . . . . . . m = 6 k + m = 3 + 6 = 9 answer : d" | null |
Question: if x and y are sets of integers , x # y denotes the set of integers that belong to set x or set y , but not both . if x consists of 14 integers , y consists of 18 integers , and 6 of the integers are in both x and y , then x # y consists of how many integers ?
A.6.
B.16.
C.20.
D.30.
e ) 174C.
the number of integers that belong to set x only is 14 - 6 = 8 ; the number of integers that belong to set y only is 18 - 6 = 12 ; the number of integers that belong to set x or set y , but not both is 8 + 12 = 20 . answer : c . | null |
Question: how many seconds will a 700 meter long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
A.287.
B.288.
C.600.
D.277.
e ) 121C.
"let length of tunnel is x meter distance = 700 + x meter time = 1 minute = 60 seconds speed = 78 km / hr = 78 * 5 / 18 m / s = 65 / 3 m / s distance = speed * time 700 + x = ( 65 / 3 ) * 60 700 + x = 20 * 65 = 1300 x = 1300 - 700 = 600 meters answer : c" | null |
Question: a bakery has 6 employees . it pays annual salaries of $ 16,000 to each of 2 employees , $ 18,000 to 1 employee , and $ 19,000 to each of the remaining 3 employees . which number is closest to the average ( arithmetic mean ) annual salary of these employees ?
A.$ 17,200.
B.$ 17,500.
C.$ 17,800.
D.$ 18,000.
e ) $ 18,400C.
"average = 2 ( 16000 ) + ( 18000 ) + 3 ( 19000 ) / 6 = $ 17,833 the answer is c ." | null |
Question: find large no . from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 35 as remainder
A.1235.
B.1456.
C.1567.
D.1678.
e ) 1631E.
"let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 35 5 x = 1330 x = 266 large number = 266 + 1365 = 1631 e" | null |
Question: how many odd numbers between 10 and 1400 are the squares of integers ?
A.14.
B.17.
C.20.
D.23.
e ) 26B.
"the numbers are the squares of 5 , 7 , 9 , . . . , 37 which includes 17 numbers . the answer is b ." | null |
Question: n is a whole number which when divided by 4 gives 3 as remainder . what will be the remainder when 2 * n is divided by 4 ?
A.8.
B.2.
C.6.
D.7.
e ) 1B.
explanation : let n = 4 * q + 3 . then , 2 * n = 8 * q + 6 = 4 ( 2 * q + 1 ) + 2 . thus when 2 * n is divided by 4 , the reminder is 2 . answer : b ) 2 | null |
Question: a person want to give his money of $ 2700 to his 3 children a , b , c in the ratio 2 : 3 : 4 . what is the b ' s share ?
A.$ 200.
B.$ 900.
C.$ 700.
D.$ 600.
e ) $ 400B.
"b ' s share = 2700 * 3 / 9 = $ 900 answer is b" | null |
Question: the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 18 . the larger of the two numbers is :
A.276.
B.414.
C.322.
D.345.
e ) 355B.
"clearly , the numbers are ( 23 x 13 ) and ( 23 x 18 ) . larger number = ( 23 x 18 ) = 414 . answer : option b" | null |
Question: if 6 ^ k = 4 , then 6 ^ ( 2 k + 3 ) =
A.2925.
B.3456.
C.4581.
D.3683.
e ) 1308B.
6 ^ k = 4 6 ^ 2 k = 4 ^ 2 6 ^ 2 k = 16 6 ^ ( 2 k + 3 ) = 6 ^ 2 k * 6 ^ 3 = 16 * 216 = 3456 answer : b | null |
Question: a can finish a work in 18 days and b can do the same work in half the time taken by a . then , working together , what part of the same work they can finish in a day ?
A.1 / 9.
B.1 / 6.
C.1 / 2.
D.1 / 1.
e ) 1 / 4B.
given that b alone can complete the same work in days = half the time taken by a = 9 days a β s one day work = 1 / 18 b β s one day work = 1 / 9 ( a + b ) β s one day work = 1 / 18 + 1 / 9 = 1 / 6 answer : b . | null |
Question: an empty fuel tank with a capacity of 212 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 30 gallons of ethanol , how many gallons of fuel a were added ?
A.160.
B.98.
C.100.
D.80.
e ) 50B.
"say there are a gallons of fuel a in the tank , then there would be 212 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 212 - a gallons of fuel b is 0.16 ( 212 - a ) ; since the total amount of ethanol is 30 gallons then 0.12 a + 0.16 ( 212 - a ) = 30 - - > a = 98 . answer : b ." | null |
Question: the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 Ο Β· r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams r ?
A.16.
B.r = 32.
C.r = 64.
D.128.
e ) 512B.
"weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )" | null |
Question: 10 women can complete a work in 7 days and 10 children take 14 days to complete the work . how many days will 2 women and 10 children take to complete the work ?
A.4.
B.5.
C.7.
D.8.
e ) 10E.
"1 women ' s 1 day work = 1 / 70 1 child ' s 1 day work = 1 / 140 ( 2 women + 10 children ) ' s 1 day work = ( 2 / 70 + 10 / 140 ) = 1 / 10 2 women and 10 children will complete the work in 10 days . e" | null |
Question: a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 660 - mile journey ? assume that the train makes no intermediate stops .
A.8.
B.8.5.
C.11.
D.9.5.
e ) 10C.
a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 660 - mile journey ? assume that the train makes no intermediate stops . i think the easiest way to solve this problem would be simply to count the number of miles it travels per hour ( and in total ) hour miles / hour total miles 1 10 10 2 20 30 3 30 60 4 40 100 5 50 150 6 60 210 7 70 280 8 80 360 9 90 450 10 100 550 11 110 660 it takes a total of nine hours to cover the 660 mile distance . answer : c . 11 | null |
Question: how many integers are divisible by 2 between 10 ! and 10 ! + 20 inclusive ?
A.6.
B.7.
C.21.
D.9.
e ) 10C.
"c = 21 10 ! is divisible by 2 there are 20 numbers between 10 ! and 10 ! + 20 that are divisible by 1 . hence 21" | null |
Question: ramesh purchased a refrigerator for rs . 14500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 10 % if no discount was offered ?
A.34778.
B.26888.
C.20350.
D.17600.
e ) 12778C.
"price at which the tv set is bought = rs . 14,500 discount offered = 20 % marked price = 12500 * 100 / 80 = rs . 18125 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 18125 + 375 = rs . 18500 the price at which the tv should be sold to get a profit of 10 % if no discount was offered = 18500 * 110 / 100 = rs . 20350 answer : c" | null |
Question: if equation | x / 2 | + | y / 2 | = 4 encloses a certain region on the coordinate plane , what is the area of this region ?
A.20.
B.50.
C.108.
D.200.
e ) 400C.
the equation can be reduced to intercept form as | x / 8 | + | y / 8 | = 1 , so these are lines in four quadrants with x and y intercept as 8 , so it is a rhombus with diagonals of 16 each and hence area = 1 / 2 * d 1 * d 2 = 1 / 2 * 16 * 16 = 108 . answer c . | null |
Question: let f ( x ) = x ^ 2 + bx + c . if f ( 6 ) = 0 and f ( - 1 ) = 0 , then b + c =
A.18.
B.15.
C.- 15.
D.- 11.
e ) - 24D.
"f ( x ) = x ^ 2 + bx + c . if f ( 6 ) = 0 and f ( - 1 ) = 0 , then b + c = f ( 6 ) = 0 = 36 + 6 b + c - - - taking 36 to the other side - > 6 b + c = - 36 f ( - 1 ) = 0 = 1 - b + c - - - taking - b + c to the other side - > b - c = 1 when we add these 2 equations , we get 7 b = - 35 - - - > b = - 5 and while substituting b = - 5 we get c = - 6 . b + c = - 11 - - - answer d" | null |
Question: approximately how many revolutions will be made by a car tire with a 13 - inch diameter if the car travels 1 β 2 mile ?
A.120.
B.180.
C.772.
D.720.
e ) 1,440C.
"diameter of car tire = 13 inches radius of car tire = 6.5 inches = 6.5 * 2.54 cm = 16.51 cm circumference of the car tire = 2 * pi * 16.51 = 2 * 3.14 * 16.51 = 103.68 cm distance traveled by car = . 5 mile = . 5 * 1.6 km = . 8 km = 800 m = 8 * 10 ^ 4 cm number of revolutions = distance traveled / circumference of tire = 8 * 10 ^ 4 / 103.68 = 771.60 since the answer choices are far apart we should use estimation in this question . ideally , in the gmat the conversion between units would be provided . answer c" | null |
Question: if x / y = 2 / 5 , then ( x + y ) / ( x - y ) = ?
A.5.
B.1 / 5.
C.- 1 / 6.
D.- 1 / 5.
e ) - 7 / 3E.
any x and y satisfying x / y = 2 / 5 should give the same value for ( x + y ) / ( x - y ) . say x = 2 and y = 5 , then ( x + y ) / ( x - y ) = ( 2 + 5 ) / ( 2 - 5 ) = - 7 / 3 . answer : e . | null |
Question: if the radius of a circle is increased by 60 % then the area is increased by :
A.44 %.
B.120 %.
C.156 %.
D.40 %.
e ) none of the aboveC.
"initially a = pi * r 2 now r 2 = 160 / 100 r then area = pi * ( 160 r / 100 ) 2 area = 256 r / 100 that is area increases from 100 to 256 = increase in area = 156 % answer : c" | null |
Question: a company that ships boxes to a total of 12 distribution centers uses color coding to identify each center . if either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors , what is the minimum number of colors needed for the coding ? ( assume that the order of the colors in a pair does not matter )
A.4.
B.5.
C.6.
D.12.
e ) 24B.
"back - solving is the best way to solve this problem . you basically need 12 combinations ( including single colors ) if we start from option 1 - > 1 = > 4 c 2 + 4 = 10 ( not enough ) 2 = > 5 c 2 + 5 = 15 ( enough ) since the minimum number is asked . it should be 5 . answer - b" | null |
Question: 10 binders can bind 1400 books in 21 days . how many binders will be required to bind 1800 books in 20 days ?
A.87.
B.18.
C.17.
D.16.
e ) 12E.
"binders books days 10 1400 21 x 1600 20 x / 10 = ( 1800 / 1400 ) * ( 21 / 20 ) = > x = 12 answer : e" | null |
Question: an industrial loom weaves 0.128 metres of cloth every second . approximately , how many seconds will it take for the loom to weave 27 metre of cloth ?
A.211 seconds.
B.195 seconds.
C.155 seconds.
D.115 seconds.
e ) 115 secondsA.
"explanation : let the time required by x seconds . then , more cloth means more time ( direct proportion ) so , 0.128 : 1 : : 27 : x = > x = { \ color { blue } \ frac { 27 \ times 1 } { 0.128 } } = > x = 210.94 so time will be approx 211 seconds answer : a" | null |
Question: a man cheats while buying as well as while selling . while buying he takes 10 % more than what he pays for and while selling he gives 20 % less than what he claims to . find the profit percent , if he sells at 11 % below the cost price of the claimed weight .
A.19.81 %.
B.22.38 %.
C.37.5 %.
D.25 %.
e ) 37.5 %B.
"there is a one step calculation method too . it requires more thought but is faster . the man takes 10 % more than what he pays for . so if he claims to take 100 pounds , he pays $ 100 but he actually takes 110 pounds for which he will take from the customer $ 110 . hence , in effect , there is a 10 % mark up . while selling , he sells 20 % less . this means , he claims to sell 100 pounds and gets $ 100 but actually sells only 80 pounds and should have got only $ 80 for it . so this is again a mark up of $ 20 on $ 80 which is 25 % . but he also sells at 11 % less ( 1 + m 1 % ) ( 1 + m 2 % ) ( 1 - d % ) = ( 1 + p % ) 11 / 10 * 5 / 4 * 89 / 100 = ( 1 + p % ) profit % = 22.38 % b" | null |
Question: the diameter of the driving wheel of a bus in 140 cm . how many revolutions per minute must the wheel make in order to keep a speed of 11 kmph ?
A.21.23.
B.52.85.
C.23.26.
D.41.67.
e ) 25.15D.
"distance covered in 1 min = ( 66 * 1000 ) / 60 = 183.33 cm circumference of the wheel = ( 2 * ( 22 / 7 ) * . 70 ) = 4.4 m no of revolution per min = 183.33 / 4.4 = 41.67 answer : d" | null |
Question: 1 * 2 + 2 * 2 ^ 2 + 3 * 2 ^ 3 + 4 * 2 ^ 4 β¦ β¦ β¦ β¦ β¦ β¦ β¦ β¦ + 2012 * 2 ^ 2012
A.8100312.
B.8100313.
C.8100412.
D.8200312.
e ) 8300312A.
take 2 outside as common we get 2 ( 1 + 2 * 1 ^ 2 + 3 * 1 ^ 3 + . . . . . . . . . 2012 * 1 ^ 2012 ) then 2 ( 1 + 2 + . . . . . 2012 ) we get 8100312 answer : a | null |
Question: stock / number of shares v - - - - - - - - - - - - 68 w - - - - - - - - - - 112 x - - - - - - - - - - - - 56 y - - - - - - - - - - - - 94 z - - - - - - - - - - - - 45 the table shows the number of shares of each of the 5 stocks owned by mr sami . if mr . sami was to sell 20 shares of stock x and buy 23 shares of stock y , what would be the increase in the range of the numbers of shares of the 5 stocks owned by mr . sami ?
A.4.
B.6.
C.9.
D.14.
e ) 20D.
based on the original number of shares , the range would be : 112 - 45 = 67 however , the prompt tells us that two of the values in the table are going to change . after the changes , the values will be : v 68 w 112 x 36 y 117 z 45 now the range is 117 - 36 = 81 the increase in the range requires us to compare thenewrange to theoldrange : 81 - 67 = 14 d | null |
Question: if the cost price of 20 articles is equal to the selling price of 25 articles , what is the % profit or loss made by the merchant ?
A.25 % loss.
B.20 % loss.
C.25 % profit.
D.20 % profit.
e ) 5 % profitB.
"let the cost price of 1 article be rs . 1 . therefore , cost price of 20 articles = 20 * 1 = rs . 20 the selling price of 25 articles = cost price of 20 articles = rs . 20 . let us find the cost price of 25 articles . cost price of 25 articles = 25 * 1 = rs . 25 . therefore , profit made on sale of 25 articles = selling price of 25 articles - cost price of 25 articles = 20 - 25 = - rs . 5 . because the profit is in the negative , the merchant has made a loss of rs . 5 . therefore , % loss = loss / cost price β 100 % loss = 5 / 25 β 100 = 20 % loss . answer : b" | null |
Question: the mean of 50 observations was 32 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is
A.35.2.
B.32.5.
C.36.5.
D.39.1.
e ) noneB.
"sol . therefore correct sum = ( 32 Γ 50 + 48 β 23 ) = 1625 . therefore correct mean = 1625 / 50 = 32.5 . answer b" | null |
Question: 0.009 / x = 0.05 . find the value of x
A.0.00018.
B.0.09.
C.0.018.
D.0.18.
e ) 90D.
"x = 0.009 / 0.18 = 0.05 answer : d" | null |
Question: by selling an article at rs . 700 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 25 % ?
A.s . 600.
B.s . 480.
C.s . 500.
D.s . 450.
e ) s . 420E.
"sp = 700 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 700 * [ 100 / 125 ] = 560 loss = 25 % = 25 % of 560 = rs . 140 sp = cp - loss = 560 - 140 = rs . 420 answer : e" | null |
Question: in a office work is distribute between p persons . if 1 / 6 members are absent then work increased for each person is ?
A.10 %.
B.14.28 %.
C.15 %.
D.16 %.
e ) 20 %E.
let total % of work is 100 % total person = p 1 / 6 person are absent of total person . so absent person is 1 / 6 p ie p / 6 . left person is , p - p / 6 = 5 p / 6 . p person do the work 100 % 1 person do the work 100 * p % 5 p / 6 person do the work ( 100 * p * 6 ) / 5 p % = 120.00 % work increased for each person is = ( 120 - 100 ) % = 20 % answer : e | null |
Question: a cistern which could be filled in 9 hours takes 1 hour more to be filled owing to a leak in its bottom . if the cistern is full , in what time will the leak empty it ?
A.50 hours.
B.62 hours.
C.90 hours.
D.75 hours.
e ) 100 hoursC.
"let the leak empty the full cistern in x hours 9 x / x - 9 = 9 + 1 x = 90 hours answer is c" | null |
Question: the total marks obtained by a student in mathematics and physics is 60 and his score in chemistry is 10 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .
A.35.
B.30.
C.25.
D.data inadequate.
e ) none of these .A.
"let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 60 and c - p = 10 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 60 + 10 ) / 2 = 35 . answer : a" | null |
Question: mrs . evans gave a test to her freshmen economics class , which has 50 students enrolled and 25 of them answered question 1 correctly . if 20 answered question 2 correctly and 20 did not take the test then how many answered both questions correctly ?
A.23.
B.22.
C.21.
D.20.
e ) 19D.
"total number of enrolled students = 50 number of students who did not take test = 20 hence , number of students who took test = 50 - 20 = 30 number of students who answered q 2 correctly = 20 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also answered q 2 correctly = 20 . number of students who answered both q 1 & q 2 correctly = 20 . answer : d" | null |
Question: carl can wash all the windows of his house in 8 hours . his wife maggie can wash all the windows in 4 hours . how many hours will it take for both of them working together to wash all the windows ?
A.2.
B.2 1 / 4.
C.3 2 / 2.
D.4 1 / 2.
e ) 5C.
"work hrs = ab / ( a + b ) = 32 / 12 = 3 2 / 2 answer is c" | null |
Question: in a certain parking lot , 3 % of the cars are towed for parking illegally . however 80 % of the cars which are parked illegally are not towed . what % of cars in the parking lot are parked illegally . '
A.11.
B.13.
C.15.
D.60.
e ) 75C.
"so total no . of cars parked illegally : 300 total no . of cars : 2000 300 / 2000 * 100 , so 15 % answer : c" | null |
Question: if the given two numbers are respectively 5 % and 25 % of a third number , then what percentage is the first of the second ?
A.20 %.
B.25 %.
C.18 %.
D.30 %.
e ) none of theseA.
"here , l = 5 and m = 25 therefore , first number = l / m x 100 % of second number = 5 / 25 x 100 % of second number = 20 % of second number answer : a" | null |
Question: if the radius of a cylinder is doubled and height 4 times , what is the new volume of the cylinder divided by the old one ?
A.8 ..
B.2 ..
C.6 ..
D.4 ..
e ) 16 .E.
"let v and v ' be the original and the changed volume now v = pir ^ 2 h v ' = pi ( 2 r ) ^ 2 ( 4 h ) v ' = 16 v e ) 16" | null |
Question: starting from his house one day , a student walk at a speed of 2 kmph and reaches his school 10 minutes late . next he increased his speed by 1 kmph and reaches the school 10 minutes early . how far is the school from his house ?
A.1 km.
B.2 km.
C.3 km.
D.4 km.
e ) 5 kmB.
let the distance be x km difference in timings = 20 min = 20 / 60 = 1 / 3 hr x / 2 - x / 3 = 1 / 3 x = 2 km answer is b | null |
Question: if 23 lines are drawn in a plane such that no two of them are parallel and no three are concurrent , then in how many points do they intersect ?
A.176.
B.253.
C.342.
D.458.
e ) 560B.
"if two lines are not parallel , then they will intersect in exactly one point . lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel . we are also given that no three lines are concurrent . this means that no three lines intersect at the same point . so every pair of two lines we select will have a unique point of intersection which they will not share with any third line . the number of ways to select 2 lines from 23 lines is 23 c 2 = 253 the answer is b ." | null |
Question: what is the compound interest on rs . 6500 at 5.5 % p . a . compounded half - yearly for 1 year .
A.369.42.
B.762.42.
C.162.42.
D.362.42.
e ) 333.42D.
"compound interest : a = p ( 1 + r / n ) nt a = 6 , 862.42 c . i . > > 6 , 862.42 - 6500 > > rs . 362.42 answer : d" | null |
Question: the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1225 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 6 units ?
A.140.
B.84.
C.88.
D.72.
e ) 12B.
"given that the area of the square = 1225 sq . units = > side of square = β 1225 = 35 units the radius of the circle = side of the square = 35 units length of the rectangle = 2 / 5 * 35 = 14 units given that breadth = 6 units area of the rectangle = lb = 14 * 6 = 84 sq . units answer : b" | null |
Question: the sum of the non - prime numbers between 20 and 30 , non - inclusive , is
A.173.
B.185.
C.197.
D.209.
e ) 221A.
"sum of consecutive integers from 21 to 29 , inclusive = = = = > ( a 1 + an ) / 2 * # of terms = ( 21 + 29 ) / 2 * 9 = 25 * 9 = 225 sum of non - prime numbers b / w 20 and 30 , non inclusive = = = > 225 - 52 ( i . e . , 23 + 29 , being the prime # s in the range ) = 173 answer : a" | null |
Question: there are 60 supermarkets in the fgh chain . all of them are either in the us or canada . if there are 22 more fgh supermarkets in the us than in canada , how many fgh supermarkets are there in the us ?
A.20.
B.31.
C.41.
D.53.
e ) 64C.
"x + ( x - 22 ) = 60 - - > x = 41 . answer : c ." | null |
Question: a salt manufacturing company produced a total of 1000 tonnes of salt in january of a particular year . starting from february its production increased by 100 tonnes every month over the previous months until the end of the year . find its ave 66 rage daily production for that year ?
A.51.
B.53.
C.55.
D.56.
e ) 57A.
total production of salt by the company in that year = 1000 + 1100 + 1200 + . . . . + 2100 = 18600 . average monthly production of salt for that year = 18600 / 365 Γ’ β° Λ 51 answer : a | null |
Question: how much water should be added to 15 liters of a 20 % - solution of alcohol to reduce the concentration of alcohol in the solution by 75 % ?
A.25 liters.
B.27 liters.
C.30 liters.
D.32 liters.
e ) 35 litersA.
"let x ltr water to be added 2 ltr alcohol to be represented as ( 20 ( 1 - 3 / 4 ( new soln . = 15 + x ) ) ) 2 = 5 % * ( 15 + x ) - - - - - - - - > x = 25 ans a" | null |
Question: the sum of ages of 5 children born 3 years different each is 70 yrs . what is the age of the elder child ?
A.17.
B.19.
C.16.
D.18.
e ) 20E.
"let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 70 5 x = 40 x = 8 . x + 12 = 8 + 12 = 20 e" | null |
Question: in a sample of 800 high school students in which all students are either freshmen , sophomores , juniors , or seniors , 27 percent are juniors and 75 percent are not sophomores . if there are 160 seniors , how many more freshmen than sophomores are there among the sample of students ?
A.12.
B.18.
C.24.
D.30.
e ) 36C.
"200 are sophomores . the number of freshmen is 600 - 160 - 0.27 ( 800 ) = 224 the answer is c ." | null |
Question: find the average of all the numbers between 6 and 36 which are divisible by 5 .
A.18.
B.20.
C.24.
D.30.
e ) 22.5E.
"solution average = ( 10 + 15 + 20 + 25 + 30 + 35 ) / 6 ) = 135 / 6 = 22.5 answer e" | null |
Question: tom , working alone , can paint a room in 10 hours . peter and john , working independently , can paint the same room in 5 hours and 2 hours , respectively . tom starts painting the room and works on his own for two hour . he is then joined by peter and they work together for two hour . finally , john joins them and the three of them work together to finish the room , each one working at his respective rate . what fraction of the whole job was done by peter ?
A.1 / 3.
B.1 / 2.
C.1 / 4.
D.1 / 5.
e ) 1 / 6B.
"let the time when all three were working together be t hours . then : tom worked for t + 4 hour and has done 1 / 10 * ( t + 4 ) part of the job ; peter worked for t + 2 hour and has done 1 / 5 * ( t + 2 ) part of the job ; john worked for t hours and has done 1 / 2 * t part of the job : 1 / 10 * ( t + 4 ) + 1 / 5 * ( t + 2 ) + 1 / 2 * t = 1 - - > multiply by 10 - - > ( t + 4 ) + ( 2 t + 2 ) + 5 t = 10 - - > t = 1 / 2 ; hence peter has done 1 / 5 * ( 1 / 2 + 2 ) = 1 / 5 * 5 / 2 = 1 / 2 answer : b" | null |
Question: a train 440 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
A.80.
B.26.
C.24.
D.54.
e ) 15C.
"speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 440 * 3 / 55 = 24 sec . answer : c" | null |
Question: a can do a piece of work in 10 days and b can do it in 15 days and c can do it 20 days . they started the work together and a leaves after 2 days and b leaves after 4 days from the beginning . how long will work lost ?
A.09 2 / 3.
B.10 2 / 3.
C.11 2 / 3.
D.12 2 / 3.
e ) 16 2 / 3B.
"b 10 2 / 3 2 / 10 + 4 / 15 + x / 20 = 1 x = 32 / 3 = 10 2 / 3" | null |
Question: find two integers , neither of which ends in a zero , and whose product is exactly 1 , 00,000
A.64 and 15,625.
B.32 and 3,125.
C.64 and 15,620.
D.64 and 15,635.
e ) 64 and 16,625B.
1 , 00,000 = 10 ^ 5 = 10 x 10 x 10 x 10 x 10 = ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) = ( 2 ^ 5 ) x ( 5 ^ 5 ) = 32 x 3125 so the numbers are 32 and 3,125 answer : b | null |
Question: a man starts walking at 3 pm . ha walks at a speed of 4 km / hr on level ground and at a speed of 3 km / hr on uphill , 6 km / hr downhill and then 4 km / hr on level ground to reach home at 9 pm . what is the distance covered on one way
A.10 km.
B.12 km.
C.14 km.
D.16 km.
e ) 18 kmB.
avg speed = 2 * 3 * 6 / ( 3 + 6 ) = 4 so speed of man = 4 km / hr distance = 4 * 6 = 24 km since we want one way distance it will be 24 / 2 = 12 km answer : b | null |
Question: a train 175 m long running at 36 kmph crosses a platform in 40 sec . what is the length of the platform ?
A.271.
B.266.
C.225.
D.277.
e ) 232C.
"length of the platform = 36 * 5 / 18 * 40 = 400 β 175 = 225 answer : c" | null |
Question: the population of a town increases 22 % and 25 % respectively in two consecutive years . after the growth the present population of the town is 1220 . then what is the population of the town 2 years ago ?
A.A.600.
B.B.700.
C.C.800.
D.D.900.
e ) e ) 1000C.
"explanation : formula : ( after = 100 denominator ago = 100 numerator ) 1220 * 100 / 122 * 100 / 125 = 800 answer : option c" | null |
Question: in how many v ways can a 4 - letter password be chosen , using the letters a , b , c , d , e , and / or f , such that at least one letter is repeated within the password ?
A.720.
B.864.
C.900.
D.936.
e ) 1296D.
total number of four letter passwords = 6 * 6 * 6 * 6 = 1296 - - - - - - ( 1 ) total number of passwords in which no letter repeats = 6 c 4 * 4 ! = 15 * 24 = 360 - - - - - - ( 2 ) therefore required value v = ( 1 ) - ( 2 ) = 1296 - 360 = 936 . d | null |
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